CM values of Green functions associated to special cycles on Shimura varieties with applications to Siegel 3-fold X2(2)

JOURNAL OF NUMBER THEORY

卷:203

Article

Yu, Peng¹ 

[1] Chinese Acad Sci, Morningside Ctr Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China

关键词: Shimura varieties;    Complex multiplication;    Siegel-Weil formula;   

DOI  :  10.1016/j.jnt.2019.04.025

来源: Elsevier

【 摘 要 】

We generalize the definition of CM cycles beyond the 'small' and 'big' CM ones studied by various authors, such as in [BY09] and [BKY12] and give a uniform formula for the CM values of Green functions associated to these special cycles in general using the idea of regularized theta lifts. Finally, as an application to Siegel 3-fold X-2(2), we can compute special values of theta functions and Rosenhain lambda-invariants at a CM cycle, which is useful for genus two curve cryptography as in [CDSLY14]. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free